The 29-year-old woman was walking into the building at Thompson and West Houston streets at 1:15 a.m. Monday when the suspect (above) followed her in, police said. Photo:

The Bloomberg administration tried to raise parking rates at municipal facilities by more than 100 percent in some cases — and then pulled back, The Post has learned.

In what has become an embarrassing fiasco, thousands of motorists who use the dozens of municipal lots and garages received letters from the Department of Transportation on Wednesday, warning of steep increases taking effect March 1.

The letters were mysteriously dated Jan. 9, two weeks earlier.

The “Dear Sir or Madam” notice had alarming news for those at the White Plains Road parking field in The Bronx: rates would be soaring from $165 every quarter to $350 — a 112 percent hike.

Parkers at the 240-space Jerome-Gun Hill garage in The Bronx were going to get hit with a 70 percent boost, from $295 to $500.

“If you no longer wish to have a quarterly parking permit at the new rate, please contact us,” added the letter, signed by Assistant Commissioner Guillermo Leiva.

Councilman James Vacca (D-Bronx), chairman of the City Council’s Transportation Committee, was dumbfounded.

It’s the third time in less than two years that DOT has attempted to dramatically raise parking rates.

After blocking two previous attempts to raise rates by triple digits, Vacca said he thought he had a commitment from the administration to cap any increase at 20 percent.

“Now DOT comes back for the third time,” fumed Vacca. “This is going to be an unbelievable hardship on many people. This is telling drivers to take a hike.”

Vacca said he called Transportation Commissioner Janette Sadik-Khan yesterday and she told him she knew nothing about the Jan. 9 rate-hike letter.

“How you could have no knowledge of the letter when it’s signed by your deputy commissioner is beyond me,” Vacca said.

“I view this as a mistake. Have we had two previous mistakes? Yes. Is this the third mistake? It appears so.”

Three hours later, the DOT relented and notified the council it was pulling back the letter.

“DOT sent letters out earlier this month in anticipation of pricing changes. A new pricing agreement was reached after the notifications were mailed and those changes will be reflected in an updated notification,” explained mayoral spokesman John McCarthy.

Like all city agencies, DOT is looking to raise revenues to avoid cuts that will be announced next week when Mayor Bloomberg releases his preliminary budget for fiscal 2014.

The first time the DOT had to retract a bid to jack up rates was in August 2011 because of outcries. The second was in November 2012, when council members forced it to issue an apology for claiming they had OK’d the hikes.